1. Field of the Invention
The invention relates to a method of reducing the convergence time of an echo canceller connected in a transceiver arrangement between one-way transmit and receive paths coupled to a two-way transmission path and used to cancel an echo signal occurring in the receive path in response to a signal supplied to the transmit path, said echo canceller comprising a transversal filter having N adjustable complex coefficients for processing a complex signal derived from the signal supplied to the transmit path and arranged to supply a real signal component, said echo canceller also comprising a difference circuit for producing a difference signal between the signal in the receive path and the output signal of the transversal filter.
2. Description of the Prior Art
Echo cancellers are used, for example, in data transmission modems whose transmit and receive paths, jointly forming a four-wire access, are coupled by a coupling circuit known as a hybrid junction in a manner such that each modem has a two-wire access to the exterior. It is a known fact that when a connection is established between two modems via their two-wire access there may be produced in the receive path of each modem an unwanted signal, called an echo signal, which is a fraction of the signal transmitted by the transmit path of the same modem and which is due to imperfections in the coupling circuit and/or to reflections in the connection. An echo canceller has for its object to cancel this echo signal automatically in order to permit full-duplex transmission between two modems connected by their two-wire access.
In an echo canceller, the coefficients of the transversal filter have to be adjusted so that they are practically equal to samples of the impulse response of the echo path, so that this filter then provides an echo copy signal which practically cancels the echo signal in the output signal from the difference circuit. During the period of transmission of the useful signal the coefficients of the transversal signal are generally adjusted iteratively in accordance with the gradient algorithm so as to minimise the mean square value of the difference signal or error signal appearing at the output of the difference circuit. Unfortunately, this method, applied to the initialization of the coefficients before the transmission of the useful signal results in a very long coefficient-convergence time, amounting to several seconds, which may not be acceptable.
In French Patent Application No. 82 10 310 filed by Applicants on June 14, 1982 and published on Dec. 16, 1983 (French Pat. No. 2528643, granted Nov. 12, 1984), a method for calculating the coefficients is described which permits rapid convergence of the echo canceller before the transmission of the useful signal. Before recalling the essentials of this method, to which the present patent application represents an improvement, it is necessary to point out that the data signal applied to the transmit path is generally transmitted by modulation of an in-phase and a quadrature-phase carrier and, for that purpose, this data signal is first encoded so as to form a complex signal D(n) which may change value at instants nT, where T is the data interval, and which is applied on the one hand to a filter for a complex signal used to produce the modulated carrier signal which is transmitted and on the other hand to the echo canceller. The transversal filter of the echo canceller is then designed to process the complex signal D(n) with the aid of complex coefficients.
A first variant of the method described in the above-mentioned patent application is appropriate to the case when, starting from the signal .epsilon..sub.R (n) received in the receive path, a complex signal .epsilon.(n) is formed such that the error signal supplied by the difference circuit of the echo canceller is formed by the difference between the complex signal .epsilon.(n) and the complex signal supplied by the transversal signal filter. With this first variant, the N complex coefficients of the echo canceller, represented by the vector matrix row C, can be obtained via the following operations:
transmission in the transmit path of a complex periodic training signal constituted by data d(n) occurring at instants nT, the data being in sequences having a period LT, where L is the number of data in each sequence and LT is at least equal to NT, and having the property: ##EQU4## for every integer i such that 1.ltoreq.i.ltoreq.N-1, d*(n) being the complex conjugate value of data d(n) of the training signal,
after the transmission of a sequence of at least N training signal data, calculation of the coefficients C for echo signal cancellation from the sequence of coefficients forms by transmission of the next sequence of L data of the training signal, in accordance with the expression: ##EQU5## C.sub.o being the vector representing the N initial coefficients of the transversal filter,
D*(n) being the vector formed by the complex conjugate values of the last N data entering the transversal filter, and PA1 .sigma. being a term for normalization of the data such that PA1 .sigma..sup.2 is a constant term representative of the power of each of the transmitted data. PA1 C.sub.o being the vector of the N initial coefficients, PA1 e.sub.R (n) being the difference signal, PA1 D*(n) being the vector of the complex conjugate values of the last N data entering the transversal filter, and PA1 .sigma..sup.2 being a constant term representing the power of each of the transmitted data.
In practice, these initial coefficients are given a value of zero so that during calculation of the coefficients C.sub.o =0 and the complex difference signal e(n) is equal to the complex signal .epsilon.(n) formed from the received signal .epsilon..sub.R (n). Under these conditions formula (2) may be written: ##EQU6##
The property of the training signal defined by formula (1) above applies both when the impulse response of the echo path comprises a d.c. component and when that impulse response does not comprise a d.c. component. If consideration is restricted to the case in which the impulse response does not comprise a d.c. component, the property required for the training signal may be, instead of formula (1), the formula (1a), namely: ##EQU7## It is then possible to use for calculation of the coefficients formula (2a) or (3a) replacing formulae (2) and (3), namely: ##EQU8##
Starting from the originating moment when generation of the training sequence commences, the N coefficients of the echo canceller may be obtained in a time equal to NT+LT=(N+L)T, NT being the maximum duration of the impulse response of the echo path, which determines the number N of coefficients, LT being the period of the training signal. The minimum convergence time is 2NT if L is chosen equal to N.
However, the method according to the above-mentioned patent application, employing this first variant, is somewhat complicated to carry out because it requires a 90.degree. phase-shifter in the received path in order to form the complex signal .epsilon.(n) from the received signal .epsilon..sub.R (n). At the same time, calculation of the coefficients necessitates multiplications of complex numbers.
In another variant of the method according to the above-mentioned patent application it is suggested, in order to avoid these complications, that the received signal .epsilon..sub.R (n) which is a real signal, be used to calculate the N complex coefficients. The coefficient-calculation method according to this second variant comprises two steps:
in the first step, the training signal D(n) having either of the aforesaid properties is transmitted and after at least N transmitted data of this signal, coefficients C.sub.1 are calculated in accordance with formula (3) in which the complex signal .epsilon.(n) is replaced by the signal .epsilon..sub.R1 (n) received in response to the signal transmitted in the course of this first step; PA0 in the second step, the same procedure is adopted, but now with a training signal D.sub.+ (n) such that D.sub.+ (n)=j.D(n) and coefficients C.sub.2 are calculated in accordance with formula (3) and replacing .epsilon.(n) by the received signal .epsilon..sub.R2 (n).
The wanted coefficients C are obtained after the second step by forming the sum C=C.sub.1 +C.sub.2. With the method according to the above-mentioned patent application using this second variant, the convergence time of the echo canceller is 2(N+L)T, with a minimum value of 4NT if L is chosen equal to N.